When we did the dolphin swim in Grand Cayman, we could bring our phones/cameras, but were required to put them in a locker before the swim began. Observation guests (it was an option on this particular excursion) were allowed to use their cameras, etc.. but were put in a spot that they really couldn't take many pictures. Of course there was a professional photographer at the dolphin center, and they charged a couple hundred bucks to get a memory stick of the images.